Final answer:
To find the angles of the rhombus, set up an equation with the angles formed by the diagonals. Solve the equation to find the value of x. Use the value of x to find the angles of the rhombus.
Step-by-step explanation:
To find the angles of the rhombus, we need to understand the relationship between the angles formed by the diagonals and the sides of the rhombus. Let's assume that the angles formed by the diagonals are 6x and 5x, where x is a constant. The sum of all the angles in a rhombus is always 360 degrees.
Since a rhombus has two pairs of congruent opposite angles, we can set up the equation: 6x + 6x + 5x + 5x = 360. Solving this equation, we get 22x = 360. Dividing both sides by 22, we find that x is approximately 16.36.
Now, we can find the angles of the rhombus. The angles formed by the diagonals are 6x = 6(16.36) = 98.16 degrees, and 5x = 5(16.36) = 81.8 degrees. Therefore, the angles of the rhombus are approximately 98.16 degrees and 81.8 degrees.